Reconstruction and rendering-based talking head synthesis methods achieve high-quality results with strong identity preservation but are limited by their dependence on identity-specific models. Each new identity requires training from scratch, incurring high computational costs and reduced scalability compared to generative model-based approaches. To overcome this limitation, we propose FIAG, a novel 3D speaking head synthesis framework that enables efficient identity-specific adaptation using only a few training footage. FIAG incorporates Global Gaussian Field, which supports the representation of multiple identities within a shared field, and Universal Motion Field, which captures the common motion dynamics across diverse identities. Benefiting from the shared facial structure information encoded in the Global Gaussian Field and the general motion priors learned in the motion field, our framework enables rapid adaptation from canonical identity representations to specific ones with minimal data. Extensive comparative and ablation experiments demonstrate that our method outperforms existing state-of-the-art approaches, validating both the effectiveness and generalizability of the proposed framework. Code is available at: \textit{https://github.com/gme-hong/FIAG}.